Method of transmitting symbols

ABSTRACT

A method of transmitting symbols of a digital transmission constellation from a set thereof, ordered from a smallest to a greatest number of bits per symbol, may include identifying a first constellation from the set that is configured to communicate with a threshold error rate and has a greatest signal-to-noise ratio smaller than a signal-to-noise ratio of a received signal. The method may also include identifying a second constellation from the set that corresponds to a constellation with a number of bits per symbol immediately greater than the first constellation. The method may further include determining first and second probabilities of use of the first and second constellations that would generate an expected number of erroneous bits corresponding to the threshold error rate. The method may further include transmitting a symbol with a constellation selected randomly between the first and second constellations according to the first and second probabilities, respectively.

FIELD OF THE INVENTION

This invention relates to digital communications, and more particularly,to a method of transmitting symbols that implements a stochasticalgorithm.

BACKGROUND OF THE INVENTION

Research in multi-carrier modulation has grown tremendously in recentyears due to the demand for high-speed data transmission over fadingchannels (e.g. power line, wireless, etc.) where inter-symbolinterference (ISI) can occur. Instead of employing single-carriermodulation with a very complex adaptive equalizer, the channel istypically divided into N sub-channels that may be essentially ISI-freeindependent Gaussian channels.

The so-called “bit loading” is a widely employed technique inmulti-carrier systems to efficiently assign bits to each carrierdepending on the signal-to-noise ratio (SNR). In general, bit loadingtechniques allow transmitting a higher number of bits over the carrierswhere the SNR is higher and a lower number of bits over the carrierswhere the SNR is lower.

To better understand the field of application, reference is made to theso-called HomePlug AV (HPAV) communication system, though any skilledreader will appreciate that the proposed approach may be applied also tosystems different from HPAV, that is herein illustrated purely as anon-limiting example.

HomePlug® (See, for example, http://www.homeplug.org/home/), anindustrial organization that comprises more than 70 companies, wasformed in 2000 to develop and standardize specifications for homenetworking technology using existing power line wiring. The lastgeneration technology of HomePlug®, called HomePlug AV (HPAV) (See forexample, HomePlug® PowerLine Alliance, “HomePlug AV baselinespecification,” Version 1.1, May 2007—“HomePlug AV white paper,”http://www.homeplug.org/tech/whitepapers/HPAV-White-Paper 050818.pdf),is a communication system where the proposed bit loading algorithm canbe applied.

In FIG. 1, the HPAV physical layer that is the basis of analysis isshown. As explained in HomePlug® PowerLine Alliance, “HomePlug AVbaseline specification,” Version 1.1, May 2007, the input bits from themedium access control (MAC) are structured by the HPAV transmitterdifferently depending on whether they are HPAV data, HPAV controlinformation, or HomePlug 1.0 control information. In the presentapplication, for the sake of simplicity, the more common HPAV dataformat will only be referred to. At the transmitter, the informationbits are scrambled and fed into a turbo convolutional encoder with acode rate R. The code rate can be R=½ or, after puncturing, R= 16/21.The coded sequences are then bit-by-bit interleaved and converted intoQAM symbols through a bit-mapper. The data symbols (belonging to unitpower constellations) are serial-to-parallel-converted for orthogonalfrequency division multiplexing (OFDM) modulation. Each OFDM carrier canbe differently loaded, depending on the bit loading algorithm, with oneof the available modulations: BPSK, QPSK, 8-QAM, 16-QAM, 64-QAM, 256-QAMand 1024-QAM. In HPAV, the OFDM modulation is implemented by using a3072-point inverse discrete Fourier transform (IDFT). Furthermore, tocomply with frequency regulatory bodies it is typically not possible touse of all the carriers. For example, according to United Statesregulations, only 917 carriers, out of the 1536 carriers from DC to 37.5MHz, can be employed for useful transmission.

To reduce the complexity of the receiver, a suitable cyclic prefix maybe used to remove both ISI and inter-channel interference (ICI). Beforean analog front end (AFE) block, which sends the resulting signal to thepower line channel, a peak limiter block may be inserted to reduce thepeak-to-average power ratio (PAPR). At the receiver the signal after anAFE block is fed to automatic gain control (AGC) and timesynchronization blocks. The cyclic prefix is removed and the OFDMdemodulation, which is implemented by the 3072-point discrete Fouriertransform (OFT), is performed. The following assumptions are made:

i) the cyclic prefix completely eliminates ISI and ICI;

ii) a perfect synchronization is guaranteed, and

iii) the channel is time invariant within each packet.

The output from the OFDM demodulator is sent to a soft-input soft-output(SISO) de-mapper, a de-interleaver, and a turbo convolutional decoder,which, in the approach of the present embodiment, implements the Bahl,Cocke, Jelinek, and Raviv (BCJR) algorithm (See for example, L. R. Bahl,J. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of linear codesfor reducing symbol error rate,” IEEE Trans. On Inform. Theory, vol. 20,pp. 284-287, March 1974) in an improved Max-Log-MAP form (See forexample, J. Vogt and A. Finger, “Improving the max-log MAP turbodecoder,” IEEE Elect. Lett., vol. 36, pp. 1937-1939, November 2000).Successively, the bits provided by the decoder are de-scrambled toreconstruct an estimation of the transmitted bits. To complete thedescription of FIG. 1, the SNR estimate module performs the estimationof the SNR starting from the signal produced by the demodulator and itis input to the bit loading block.

The problem of bit loading has been widely studied in the literature,and it is part of a more general problem that is the possibility ofredistributing the power and the bits available over the variouscarriers, as a function of the SNR, to improve the overall performanceof the system.

A milestone method, the “water filling” algorithm (See for example, R.G. Gallager, Information theory and reliable communication, New York,Wiley, 1968), has been known to generate the optimal energy distributionand to achieve the maximum capacity. However, even if it yields theoptimal energy distribution, the maximum capacity could be achieved onlyif an infinite granularity in constellation size is assumed, which isnot realizable. For this reason, suboptimal approaches have beenstudied, such as, for example, in J. A. C. Bingham, “Multicarriermodulation for data transmission: an idea whose time has come,” IEEEComm. Magazine, pp. 5-14, May 1990, but the proposed approach is veryslow for applications that transmit over a large number of carriers andwhere a high number of bits can be loaded in each symbol. In the past,the loading issue has been analyzed using two main different approaches(See for example, J. Campello, “Optimal discrete bit loading formulticarrier modulation systems,” IEEE Symp. Info. Theory, pp. 193,August 1998), referred to as “bit rate maximization” and “marginmaximization”, respectively. The bit rate maximization approach aims atmaximizing the overall throughput of the system with a constraint on thetransmission power. (See for example, A. Leke and J. M. Cioffi, “Amaximum rate loading algorithm for discrete multitone modulationsystems,” IEEE Globecom 1997, pp. 1514-1518, November 1997, and B. S.Krongold, K. Ramchandran and D. L. Jones, “Computationally efficientoptimal power allocation algorithms for multicarrier communicationsystems,” IEEE Trans. on Comm., pp. 23-27, Jan. 2000).

The margin maximization approach aims, instead, at minimizing thetransmission power with a constraint on the overall throughput of thesystem. (See for example, P. S. Chow, J. M. Cioffi and J. A. C. Bingham,“A practical discrete multitone transreceiver loading algorithm for datatransmission over spectrally shaped channels,” IEEE Trans. on Comm., pp.773-775, April 1995, R. F. H. Fisher and J. B. Huber, “A new loadingalgorithm for discrete multitone transmission,” IEEE Globecom 1996, pp.724-728, November 1996, J. Campello, “Practical bit loading for DMT,”IEEE ICC 1999, pp. 801-805, June 1999, and N. Papandreou and T.Antonakopoulos, “A new computationally efficient discrete bit-loadingalgorithm for DMT applications,” IEEE Trans. On Comm., pp. 785-789, May2005). The proposed approaches are based on the possibility ofredistributing the power and the bits over the various carriers. Otherexamples of algorithms where power and bit loading issues are jointlystudied can be found in D. Matas and M. Lamarca, “Optimum powerallocation and bit loading with code rate constraint,” IEEE SPAWC 2009,pp. 687-691, June 2009, and H. Y. Qing and P. Q. C. M. Jiao, “Anefficient bit and power allocation algorithm for multi-carrier systems,”IEEE ICCCAS 2009, pp. 100-103, July, 2009.

On the other hand, communication systems can be subject to regulationsthat do not allow power allocation. A typical example is the HomePlug AV(HPAV) system, where the algorithms described above cannot be applied.In fact, these systems with uniform (non-adaptive) power allocation arein the field of application of the approach proposed in the presentapplication.

In this case, suitable bit loading algorithms are described in A. M.Wyglinski, F. Labeau, and P. Kabal, “Bit loading with BER-constraint formulticarrier systems,” IEEE Trans. on Wireless Comm., pp. 1383-1387,July 2005, E. Guerrini, G. Dell'Amico, P. Bisaglia and L. Guerrieri,“Bit-loading algorithms and SNR estimates for HomePlug AV,” IEEE ISPLC2007, pp. 77-82, March 2007, U.S. Patent Application Publication No.2009/0135934 to Guerrieri et al., and A. Maiga, J.-Y. Baudais and J.-F.Hélard, “Very high bit rate power line communications for homenetworks,” IEEE ISPLC 2009, pp. 313-318, March 2009.

All these approaches aim at maximizing the overall throughput of thesystem, guaranteeing, at the same time, that the bit error rate (BER)remains below a given threshold, hereafter referred to as a target BER.In A. M. Wyglinski, F. Labeau and P. Kabal, “Bit loading withBER-constraint for multicarrier systems,” IEEE Trans. on Wireless Comm.,pp. 1383-1387, July 2005, and E. Guerrini, G. Dell'Amico, P. Bisagliaand L. Guerrieri, “Bit-loading algorithms and SNR estimates for HomePlugAV,” IEEE ISPLC 2007, pp. 77-82, March 2007, different techniques havebeen proposed for multi-carrier uncoded systems. However, if applied toa coded system, they do not exploit the error-correction capabilities ofthe code, which means that the target BER is satisfied with a largemargin, but at the expense of a reduction in terms of throughput.

In U.S. Patent Application Publication No. 2009/0135934 to Guerrieri etal., a bit loading algorithm that aims at exploiting the errorcapability of the turbo code using a metric based on the LLRs ispresented. Although the achieved performance is relatively good, theiterative nature of the algorithm implies a high computationalcomplexity. The approach proposed in A. Maiga, J.-Y. Baudais and J.-F.Hélard, “Very high bit rate power line communications for homenetworks,” IEEE ISPLC 2009, pp. 313-318, March 2009, can be applied to alinear precoded discrete multitone modulation (LP-DMT) system, whichimplements a combination of multi-carrier and spread spectrumtechniques. In the contest of bit loading and turbo code there is stillthe need of an algorithm that efficiently exploits the error-correctioncapability of the code, but that has a reduced complexity.

SUMMARY OF THE INVENTION

A method of transmitting symbols of a digital transmission constellationthat allows an increase in the transmission throughput with apre-established bit-error rate or block error rate is described.Differently from the classic bit loading algorithms, the algorithm ofthe present embodiments may be not fully deterministic, but comprises astochastic operation for deciding whether to transmit symbols accordingto a first constellation or to a second constellation. More precisely,the novel method comprises the steps of:

a) identifying a first digital transmission constellation m of anordered set, that allows a communication with a pre-established maximumbit-error-rate or block-error-rate β^((T)) and with the greatestsignal-to-noise ratio smaller than the signal-to-noise ratio of thereceived signal γ;

b) identifying a second digital transmission constellation {hacek over(m)} of the ordered set that corresponds to the constellation with thenumber of bits per symbol immediately greater than that of the firstdigital transmission constellation m;

c) determining a first probability of use 1−P of the first digitaltransmission constellation and a second probability of use P of thesecond digital transmission constellation that would make the expectednumber of received erroneous bits corresponding to the pre-establishedmaximum bit-error-rate or block-error-rate β^((T)). The secondprobability may be complementary to the first probability and may bedetermined as a function of the bit-error-rates or block-error-rate ofthe first P_(e) ^((m))(γ) digital transmission constellations and secondP_(e) ^(({hacek over (m)}))(γ) corresponding to the signal-to-noiseratio of the received signal γ, and to the number of bits of a symbol ofthe first constellation m and of the second constellation {hacek over(m)};

d) transmitting a symbol with a digital transmission constellationselected randomly between the constellations first and second accordingto the respective probabilities of use first 1−P and second P.

The algorithm may be advantageously used for transmitting a plurality ofsymbols in a multi-carrier modulation system or in a HomePlug AV system.The algorithm may be implemented by a computer or processor executing asoftware program.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram for a HPAV physical layer, for datatransmission in accordance with the prior art.

FIG. 2 is a graph comparing the BLER vs. SNR of an HPAV system, withcode rate R=½, over an AWGN channel when the JPC bit loading algorithmis applied with a target BLER of 10⁻¹ and a jump probability of 0.25 inaccordance with the present invention.

FIG. 3 is an enlarged view of FIG. 2 where the SNRs that achieve thetarget BLER are highlighted for BPSK, QPSK and 8-QAM constellations,which are γ₁ ^(0.25)=−0.9671 dB, γ₂ ^(0.25)=1.8756 dB and γ₃^(0.25)=4.7629 dB, respectively.

FIG. 4 is a graph of the probability of a jump vs. SNR of the HPAVsystem, with code rate R=½, over an AWGN channel with a target BLER of10⁻¹ in accordance with the present invention.

FIG. 5 depicts a graph of the throughput vs. SNR over an AWGN channelfor R=½ in the case of the JPC in accordance with the present inventionand the prior art BTC bit loading algorithms when a target BLER of 10⁻¹is considered.

FIG. 6 is a graph of the BLER vs. SNR over an AWGN channel for R=½ inthe case of the JPC in accordance with the present invention and theprior art ETC bit loading algorithms when a target BLER of 10⁻¹ isconsidered.

FIG. 7 is a graph of the throughput vs. SNR over an AWGN channel for R=16/21 in the case of the JPC in accordance with the present inventionand the prior art ETC bit loading algorithms when a target BLER of 10⁻¹is considered.

FIG. 8 is a graph of the BLER vs. SNR over an AWGN channel for R= 16/21in the case of the JPC in accordance with the present invention and theprior BTC bit loading algorithms when a target BLER of 10⁻¹ isconsidered.

FIG. 9 is a graph of the throughput vs. SNR over the OPERA channel model1 for R=½ in the case of the JPC in accordance with the presentinvention and the prior BTC bit loading algorithms when a target BLER of10⁻¹ is considered.

FIG. 10 is a graph of the BLER vs. SNR over the OPERA channel model 1for R=½ in the case of the JPC in accordance with the present inventionand the prior BTC bit loading algorithm when a target BLER of 10⁻¹ isconsidered.

FIG. 11 is a graph of the throughput vs. SNR over the OPERA channelmodel 1 for R= 16/21 in the case of the JPC in accordance with thepresent invention and the prior BTC bit loading algorithms when a targetBLER of 10⁻¹ is considered.

FIG. 12 is a graph of the BLER vs. SNR over the OPERA channel model 1for R= 16/21 in the case of the JPC in accordance with the presentinvention and the prior BTC bit loading algorithms when a target BLER of10⁻¹ is considered.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The bit loading algorithm disclosed herein, that may be classified as analgorithm that aims at increasing the throughput while achieving anoverall target BER or, alternatively, an overall target block error rate(BLER) with a relatively uniform power allocation, efficiently exploitsthe error-correction capability of the code and has a reducedcomplexity. Differently from the known bit loading techniques based ondeterministic rules, the algorithm contemplates a probabilistic approachand it may be applied to both coded and uncoded systems.

Before introducing the bit loading algorithm, hereinafter referred asthe Jump Probability Computation (JPC) algorithm, the prior BTC bitloading algorithm disclosed in, U.S. Patent Application Publication No.2009/0135934 to Guerrieri at al., is revisited, to better understand howthe algorithm operates.

The following nomenclature will be used:

N: number of carriers;

k: carrier index, k=1, 2, . . . , N;

m_(k): number of bits loaded on the k-th carrier;

γ_(k): SNR of the k-th carrier;

β^((T)): fixed target BER or BLER

γ^((m) ^(k) ^(,T)): SNR limit value to achieve the fixed target β^((T))when m_(k) bits are loaded on the k-th carrier; and

C: set of all the possible numbers of bits that can be mapped.

BER Threshold Constant (BTC) Algorithm

The prior art BTC algorithm attempts to increase the overall throughputof the system with a uniform power allocation, achieving a target BER(or BLER) per carrier. In general, the BER (or BLER) performance of asystem as a function of the SNR can be obtained by simulations. Forexample, in L. Guerrieri, P. Bisaglia, G. Dell'Amico and E. Guerrini,“Performance of the turbo coded HomePlug AV system over power-linechannels,”IEEE ISPLC 2007, pp. 138-143, March 2007 it has been computedfor the coded HPAV system. Consequently, for each constellation, an SNRlimit value can be fixed for a given target BER (or BLER).

The problem solved by the BTC is:

$\begin{matrix}\left\{ {{{\begin{matrix}{\max\limits_{m_{k} \in C}m_{k}} \\{{s.t.\gamma_{k}} \geq \gamma^{({m_{k},T})}}\end{matrix}\mspace{14mu} k} = 1},2,\ldots\mspace{14mu},N} \right. & (1)\end{matrix}$

The algorithm may optionally employ a memory look-up table that includesthe SNR limit value for each allowable modulation.

In ideal conditions, i.e., when any estimation is not performed and thechannel state information (CSI) is assumed to be known at the receiver,the BTC algorithm is a conservative bit loading. That means that thetarget BER (or BLER) is achieved with a large margin and with aconsequent loss in throughput.

The Algorithm of the Present Embodiments

The algorithm, herein referred as “Jump Probability Computationalgorithm” (JPC), starts from an allocation based on the BTC and it mayincrease the throughput and reduce the margin over the overall targetBER (or BLER).

In the JPC algorithm, after the constellation assignment based on theclassic BTC algorithm, a “jump” is made into the constellation of theimmediately higher order depending on an appropriate probability definedfor each carrier, while still achieving the overall target BER (or BLER)of the system.

Let P_(k) be the probability of a jump into the constellation of theimmediately higher order for the k-th carrier and let p_(k) be a randomvariable uniformly distributed within [0, 1]. The JPC algorithm may bedetailed in the following steps:

1. Evaluate a first bit allocation {m_(k)} based on the BTC algorithm;

2. Determine the bit allocation {{hacek over (m)}_(k)} that correspondsto the immediately higher constellation, with {hacek over (m)}_(k)εC;

3. Given the SNR over each carrier {γ_(k)}, compute the respectiveprobability of jump {P_(k)}. The computation of {P_(k)} will bedescribed hereinafter;

4. Generate {p_(k)}εU[0, 1]; and

5. The final bit allocation {q_(k)} is given by

$\begin{matrix}{q_{k} = \left\{ {{{\begin{matrix}m_{k} & {{{if}\mspace{14mu} p_{k}} > P_{k}} \\\overset{\Cup}{m} & {{{if}\mspace{14mu} p_{k}} \leq P_{k}}\end{matrix}\mspace{14mu} k} = 1},2,\ldots\mspace{14mu},N} \right.} & (2)\end{matrix}$

It should be noted that the target BER (or BIER) is achieved only if thenumber of realizations is large enough to have reliable statistics. Thismeans that the target is achieved over each carrier after a properobservation time and it is achieved per groups of carriers if the numberof carriers is sufficiently large. Hereinafter the computation of P_(k)is explained.

The computation of P_(k), the probability of a jump into theconstellation of the immediately higher order for the k-th carrier, isan issue that may be of particular importance for the JPC bit loadingalgorithm, since the performance of the algorithm depends on theaccuracy of P_(k). Furthermore, a fast computation may be fundamentalfor an efficient implementation of the proposed approach. In general,referring to the k-th carrier, P_(k) depends on the fixed target BER (orBLER) β^((T)), on the SNR γ_(k), and on the constellations associatedwith m_(k) and {hacek over (m_(k))}. For the computation of theprobability of a jump, an additive white Gaussian noise (AWGN) channelmay be considered, where the SNR γ_(k) is the same for each carrier,i.e. γ_(k)=γ with k=1, 2, . . . , N. In an AWGN channel, the bitallocation is the same for each carrier, hence the carrier index can beneglected m_(k)=m, and also P_(k) is the same for each carrier P_(k)=P,with k=1, 2, . . . , N. Hereinafter, different procedures to compute Pgiven γ are described. In specific cases, if the BER (or BLER) can beexpressed in a closed-form, the value of P may be analytically computed.For all the other cases, an alternative procedure is implemented.

To apply the above procedure, the closed-form expressions of the BER (orBLER) as a function of the SNR should typically be available for all theconsidered constellations. If this assumption is verified, let β^((T))be the fixed target BER and let γ^((m,T)) and γ^(({hacek over (m)},T))be the SNR thresholds of the BTC algorithm that allow loading m and{hacek over (m)} bits, respectively. For eachγε(γ^((m,T)),γ^(({hacek over (m)},T))), the probability of a jump fromthe constellation that loads m bits to the constellation that loads{hacek over (m)} bits is computed. In a multi-carrier system with Navailable carriers, the total number of loaded bits isn=n ^((m)) +n ^(({hacek over (m)}))  (3)where n^((m)) and n^(({hacek over (m)})) are the number of bits mappedover the carriers that load m and {hacek over (m)} bits, respectively.Assuming a probability of a jump {tilde over (P)}, these parameters canbe expressed as followsn ^((m))=(1−{tilde over (P)})·m·N  (4)n ^(({hacek over (m)})) ={tilde over (P)}·{hacek over (m)}·N  (5)

With this bit loading, the overall BER, {tilde over (β)}, is given by

$\begin{matrix}{\overset{\sim}{\beta} = {{{P_{e}^{(m)}(\gamma)} \cdot \frac{n^{(m)}}{n}} + {{P_{e}^{(\overset{\Cup}{m})}(\gamma)} \cdot \frac{n^{(\overset{\Cup}{m})}}{n}}}} & (6)\end{matrix}$where P_(e) ^((m))(γ) and P_(e) ^(({hacek over (m)}))(γ) are the BERassociated with the constellations of m and {hacek over (m)} bits,respectively, at an SNR of γ. Substituting (3)-(5) in (6), the overallBER becomes

$\begin{matrix}{\overset{\sim}{\beta} = \frac{{{P_{e}^{(m)}(\gamma)} \cdot \left( {1 - \overset{\sim}{P}} \right) \cdot m} + {{P_{e}^{(\overset{\Cup}{m})}(\gamma)} \cdot \overset{\sim}{P} \cdot \overset{\Cup}{m}}}{{\left( {1 - \overset{\sim}{P}} \right) \cdot m} + {\overset{\sim}{P} \cdot \overset{\Cup}{m}}}} & (7)\end{matrix}$hence we have

$\begin{matrix}{\overset{\sim}{P} = \frac{\left( {{P_{e}^{(m)}(\gamma)} - \overset{\sim}{\beta}} \right) \cdot m}{{\left( {{P_{e}^{(m)}(\gamma)} - \overset{\sim}{\beta}} \right) \cdot m} - {\left( {{P_{e}^{(\overset{\Cup}{m})}(\gamma)} - \overset{\sim}{\beta}} \right) \cdot \overset{\Cup}{m}}}} & (8)\end{matrix}$

The probability of jump, P, that achieves the fixed target BER is thevalue that satisfies equation (8) when {tilde over (β)}=β^((T)), and itis given by:

$\begin{matrix}{P = \frac{\left( {{P_{e}^{(m)}(\gamma)} - \beta^{(T)}} \right) \cdot m}{{\left( {{P_{e}^{(m)}(\gamma)} - \beta^{(T)}} \right) \cdot m} - {\left( {{P_{e}^{(\overset{\Cup}{m})}(\gamma)} - \beta^{(T)}} \right) \cdot \overset{\Cup}{m}}}} & (9)\end{matrix}$

An example of a system where the analytical procedure can be applied isan uncoded system. In N. Benvenuto and G. Cherubini, Algorithms forcommunications systems and their applications, John Wiley & Sons,Chichester, U.K., 2002. the closed-form expressions of BER, as afunction of the SNR, are computed for PAM, QAM, PSK and FSK modulations.

In general, the BER (or BLER) closed-form expressions may be unavailableor too complex to be efficiently used. Therefore, an alternativeapproach may be proposed. A general procedure, based on simulations, tocompute P for a given γ is by the following:

I. Fix the target BER (or BLER).

II. Define a range of SNRs of interest, which includes all the SNRswhere the available constellations can properly work, namely[γ^(LOW),γ^(HIGH)]. The range of SNRs of interest may depend on theconsidered system, in particular, on its architecture (modulations anddemodulation types, coding and decoding schemes etc.).

III. Define a set of SNRs, which belong to [γ^(LOW),γ^(HIGH)], hereafterreferred as Ω. The number of the elements of the set influences theaccuracy of the computation of P: the higher the number is, the betterthe accuracy is.

IV. Fix an arbitrary value for the probability of jump, P. The initialassigned value, P, and the following assigned values indicated in pointVII, can be arbitrary selected within the range (0, 1).

V. For each γεΩ:

a. Evaluate the bit allocation {m} based on the BTC algorithm.

b. Apply the JPC algorithm with the probability of jump P, obtaining thebit allocation { q}.

c. Compute, by simulations, the overall BER (or BLER) of the system withthe bit allocation { q}.

VI. Store the SNRs that achieve the target BER (or BLER), hereafterreferred as γ_({m}) ^(P) . Note that there is an SNR for eachconstellation.

VII. Repeat point V-VI for other L values of P. Let { P₁ , P₂ , . . . ,P_(L) } be the considered values of the jump probability. The values

={( P₁ ,γ_({m}) ^(P) ¹ ), ( P₂ ,γ_({m}) hu P ² ), . . . , ( P_(L),γ_({m}) hu P ^(L) ):∀mεC} are stored.

VIII. Given an SNR {tilde over (γ)}εΩ, interpolate the points stored in

in order to compute the relative probability of jump {tilde over (P)}.

To clarify the procedure, an example of the computation of theprobability of a jump is given in the case of the HPAV system. First,let us fix a target BLER of 10⁻¹, as in point I. Considering theaforementioned target BLER, a reasonable range of SNRs, Ω, for the HPAVsystem could be [−5 dB, 20 dB] in the case of R=½ and [0 dB, 35 dB] inthe case of R= 16/21(point II). For the sake of simplicity, the exampleis explained for the R=½ case only, but it can be easily extended to theR= 16/21 case. According to point III, the set of SNRs is formed by theSNRs within the range [−5 dB, 20 dB] with a step of 0.1 dB. First, theprobability of a jump P is set equal to 0.25 (point IV). Furthermore,for all the SNRs of the set, the BTC algorithm is applied (point V-a),the final bit allocation given by the JPC algorithm is evaluated (pointV-b), and the overall BLER of the system is computed (point V-c). InFIG. 2, the BLER, as a function of the SNR, achieved performing the JPCalgorithm with a jump probability of 0.25, is shown for each availableconstellation of the HPAV system.

The labels correspond to the constellation loaded by the BTC, but therespective curves may not be obtained with this constellation only. Forexample, the “BPSK” curve may be obtained randomly loading about 75% ofBPSK and 25% of QPSK, accordingly to the jump probability of 0.25. The1024-QAM is not present since in HPAV system it is not possible to jumpinto a higher constellation. Still referring to FIG. 2, the SNRs thatachieve the fixed target BLER with a jump probability of 0.25, γ_({m})^(0.25), are selected for each constellation (point VI). FIG. 3 is anenlargement of FIG. 2 where the SNRs that achieve the target BLER with ajump probability of 0.25 for the BPSK, QPSK, and 8-QAM are highlighted.

Steps V-VI are repeated for different jump probabilities, namely 0.5 and0.75, and the values of γ_({m}) ^(0.5) and γ_({m}) ^(0.75) are computedand stored (point VII). According to point VIII, as illustrated in FIG.4, it may be possible to compute the probability of a jump associatedwith a generic SNR within the range [−5 dB, 20 dB] by interpolating thepoints obtained up to now, which correspond to the marks of the curves.In particular, in FIG. 4, a linear interpolation has been used.

For example, at an SNR of 0 dB, the probability of a jump from a BPSKinto a QPSK is about 0.55 while at an SNR of 10 dB the probability of ajump from a 16-QAM into a 64-QAM is about 0.85.

We observe that, in the reported example, three values of γ_({m}) ^(P)for each constellation have been calculated, which means 18 values intotal. The values γ_({m}) ⁰ and γ_({m}) ¹ correspond to the SNRthresholds stored in the look-up table of the BTC algorithm, hence theyare already available without the further computation. This computationcan be made off-line, while the real-time processing of the signal maybe limited to an interpolation. Therefore, the increase in complexity ofthe JPC with respect to the BTC algorithm is given by the uniform randomnumber generator and the interpolating function. Achieving an accurateestimation of the probability of a jump for each SNR of interest may beof particular importance to enhance the performance of the JPCalgorithm. In general, if the number of values computed off-line isrelatively high, a coarse interpolation may be sufficient. On the otherhand, if the number of these values is low, a more complex interpolationmay be desired.

Numerical Results

The JPC bit loading algorithm applied to the HPAV system has beensimulated and its performance is shown in terms of throughput and BLERversus SNR. For comparison purposes, the performance of the BTC bitloading algorithm is also reported.

In the following simulations, a target BLER of 10⁻¹ is fixed, and theideal case of the CSI known at the receiver is considered. First, anAWGN channel is considered. In FIG. 5 and in FIG. 6, the throughput andthe BLER versus the SNR are shown, respectively, in the case of coderate R=½.

The classic ETC algorithm achieves the target with a relatively largemargin, being the BLER almost null for all the SNR values. On the otherhand, the JPC algorithm presents a BLER very close to the target,increasing the throughput compared to the BTC case. In FIG. 7 and inFIG. 8, similar results are depicted for the code rate R= 16/21.

To investigate the proposed approach under a more realistic environment,a power line channel model is introduced. In particular, the multipathchannel model proposed by the open power line communication Europeanresearch alliance (OPERA) project is considered. (See for example,“OPERA project,” http://www.ist-opera.org, and M. Babic, M. Hagenau, K.Dostert and J. Bausch, “Theoretical postulation of PLC channel model,”OPERA, Tech. Rep., March 2005). In particular, the OPERA channel model 1is employed, while the noise is AWGN. The throughput is calculated byaveraging the allocated bits of the bit loading algorithms over manyrealizations of the considered channel model. In FIG. 9 and in FIG. 10the throughput and the BLER versus the SNR are shown, respectively, inthe case of the code rate R=½.

In FIG. 9, a gain in throughput of the JPC algorithm compared to the BTCis observed at every SNR; for example, at 15 dB it is almost 10 Mb/s.The gain is coupled with a reduction of the margin over the target BLER,as depicted in FIG. 10. In FIG. 11 and in FIG. 12, the throughput andthe BLER versus the SNR are shown, respectively, in the case of the coderate R= 16/21.

Similar results are observed. In particular, a gain in throughput of theJPC algorithm compared to the BTC is observed at every SNR, as shown inFIG. 11, with a gain of approximately 12 Mb/s at 20 dB. Moreover, FIG.12 shows that the BLER is almost null in the BTC case, while it is veryclose to the target in the JPC case.

That which is claimed:
 1. A method of transmitting symbols of a digitaltransmission constellation, the digital transmission constellationbelonging to a set of digital transmission constellations ordered from aconstellation with a smallest number of bits per symbol up to aconstellation with a greatest number of bits per symbol, each digitaltransmission constellation having known respective error rate vs.signal-to-noise characteristics, the method comprising: identifying anumber of bits m of a first digital transmission constellation from theset of digital transmission constellations that is configured tocommunicate up to a threshold error rate β^((T)) and having a greatestsignal-to-noise ratio smaller than a signal-to-noise ratio of a receivedsignal γ; identifying a number of bits {hacek over (m)} of a seconddigital transmission constellation from the set of digital transmissionconstellations that corresponds to a digital transmission constellationwith a number of bits per symbol greater than the number of bits m ofthe first digital transmission constellation; determining a firstprobability of use 1−P of the first digital transmission constellationand a second probability of use P of the second digital transmissionconstellation that would generate an expected number of receivederroneous bits corresponding to the threshold error rate β^((T)), thesecond probability of use being complementary to the first probabilityof use and being determined as a function of the error rate of the firstand second digital transmission constellations P_(e) ^((m))(γ) P_(e)^(({hacek over (m)}))(γ) corresponding to the signal-to-noise ratio ofthe received signal γ and the number of bits m of the first digitaltransmission constellation and the number of bits {hacek over (m)} ofthe second digital transmission constellation; and transmitting a symbolwith a digital transmission constellation selected randomly between thefirst and second digital constellations according to the first andsecond probabilities of use 1−P, P, respectively.
 2. The method of claim1, wherein the error rate comprises one of a bit-error-rate and ablock-error-rate.
 3. The method of claim 1, wherein the secondprobability of use P is determined according to the following equation:$P = {\frac{\left( {{P_{e}^{(m)}(\gamma)} - \beta^{(T)}} \right) \cdot m}{{\left( {{P_{e}^{(m)}(\gamma)} - \beta^{(T)}} \right) \cdot m} - {\left( {{P_{e}^{(\overset{\Cup}{m})}(\gamma)} - \beta^{(T)}} \right) \cdot \overset{\Cup}{m}}}\;.}$4. The method of claim 1, wherein the second probability of use P isdetermined by at least: determining a first discrete set of values (Ω)of the signal-to-noise ratio of the received signal; determining asecond discrete set of probability values ({ P₁ , P₂ , . . . , P_(L) })of the second probability of use; filling in a look-up table ofsignal-to-noise ratio limit values for each combination of a value (P_(i) ) of the second discrete set with a digital transmissionconstellation of the set of digital transmission constellations by atleast for each signal-to-noise ratio of the received signal of the firstdiscrete set (Ω) determining an average number of bits of a symbol to betransmitted as an average of the number of bits {hacek over (m)} of asymbol of the second digital transmission constellation and the numberof bits m of the first digital transmission constellation weighted withthe second probability of use ( P_(i) ) of the second discrete set andthe complementary value thereof (1− P_(i) ), respectively, andestimating the error rate corresponding to an average number of bits ofa symbol and of a value of the first discrete set, and for thecombination of a value ( P_(i) ) of the second discrete set with thedigital transmission constellation, storing a signal-to-noise ratiolimit value configured to communicate at the threshold error rateβ^((T)); and determining the second probability of use P as a functionof the signal-to-noise ratio of the received signal γ, by one of readingfrom the look-up table a probability value corresponding to thesignal-to-noise ratio of the received signal γ and interpolatingprobability values corresponding to the signal-to-noise ratios limitvalues closest to the signal-to-noise ratio of the received signal γ. 5.The method of claim 1, wherein the set of digital transmissionconstellations comprises at least one of BPSK, QPSK, 8-QAM, 16-QAM,64-QAM, 256-QAM and 1024-QAM.
 6. The method of claim 1, wherein thesymbols are transmitted according to a multi-carrier modulation; andwherein the steps of the method are executed for each used carrier.
 7. Anon-transitory computer-readable medium for use with circuit configuredto transmit symbols of a digital transmission constellation, the digitaltransmission constellation belonging to a set of digital transmissionconstellations ordered from a constellation with a smallest number ofbits per symbol up to a constellation with a greatest number of bits persymbol, each digital transmission constellation having known respectiveerror rate vs. signal-to-noise characteristics, the computer-executableinstructions for causing the circuit to perform the method comprising:identifying a number of bits m of a first digital transmissionconstellation from the set of digital transmission constellations thatis configured to communicate up to a threshold error rate β^((T)) andhaving a greatest signal-to-noise ratio smaller than a signal-to-noiseratio of a received signal γ; identifying a number of bits {hacek over(m)} of a second digital transmission constellation from the set ofdigital transmission constellations that corresponds to a digitaltransmission constellation with a number of bits per symbol greater thanthe number of bits m of the first digital transmission constellation;determining a first probability of use 1−P of the first digitaltransmission constellation and a second probability of use P of thesecond digital transmission constellation that would generate anexpected number of received erroneous bits corresponding to thethreshold error rate β^((T)), the second probability of use beingcomplementary to the first probability of use and being determined as afunction of the error rate of the first and second digital transmissionconstellations P_(e) ^((m))(γ) P_(e) ^(({hacek over (m)}))(γ)corresponding to the signal-to-noise ratio of the received signal γ andthe number of bits m of the first digital transmission constellation andthe number of bits {hacek over (m)} of the second digital transmissionconstellation; and transmitting a symbol with a digital transmissionconstellation selected randomly between the first and second digitalconstellations according to the first and second probabilities of use1−P, P, respectively.
 8. The non-transitory computer-readable medium ofclaim 7, wherein the error rate comprises one of a bit-error-rate and ablock-error-rate.
 9. The non-transitory computer-readable medium ofclaim 7, wherein the computer-executable instructions are for causingthe circuit to determine the second probability of use P according tothe following equation:$P = {\frac{\left( {{P_{e}^{(m)}(\gamma)} - \beta^{(T)}} \right) \cdot m}{{\left( {{P_{e}^{(m)}(\gamma)} - \beta^{(T)}} \right) \cdot m} - {\left( {{P_{e}^{(\overset{\Cup}{m})}(\gamma)} - \beta^{(T)}} \right) \cdot \overset{\Cup}{m}}}\;.}$10. The non-transitory computer-readable medium of claim 7, wherein thecomputer-executable instructions for causing the circuit to determinethe second probability of use P by at least: determining a firstdiscrete set of values (Ω) of the signal-to-noise ratio of the receivedsignal; determining a second discrete set of probability values ({ P₁ ,P₂ , . . . , P_(L) }) of the second probability of use; filling in alook-up table of signal-to-noise ratio limit values for each combinationof a value ( P_(i) ) of the second discrete set with a digitaltransmission constellation of the set of digital transmissionconstellations by at least for each signal-to-noise ratio of thereceived signal of the first discrete set (Ω) determining an averagenumber of bits of a symbol to be transmitted as an average of the numberof bits {hacek over (m)} of a symbol of the second digital transmissionconstellation and the number of bits m of the first digital transmissionconstellation weighted with the second probability of use ( P_(i) ) ofthe second discrete set and the complementary value thereof (1− P_(i) ),respectively, and estimating the error rate corresponding to an averagenumber of bits of a symbol and of a value of the first discrete set, andfor the combination of a value ( P_(i) ) of the second discrete set withthe digital transmission constellation, storing a signal-to-noise ratiolimit value configured to communicate at the threshold error β^((T));and determining the second probability of use P as a function of thesignal-to-noise ratio of the received signal γ, by one of reading fromthe look-up table a probability value corresponding to thesignal-to-noise ratio of the received signal γ and interpolatingprobability values corresponding to the signal-to-noise ratios limitvalues closest to the signal-to-noise ratio of the received signal γ.11. The non-transitory computer-readable medium of claim 7, wherein theset of digital transmission constellations comprises at least one ofBPSK, QPSK, 8-QAM, 16-QAM, 64-QAM, 256-QAM and 1024-QAM.
 12. Thenon-transitory computer-readable medium of claim 7, wherein the symbolsare transmitted according to a multi-carrier modulation; and wherein thecomputer-executable instructions are for causing the circuit to executefor each used carrier.
 13. A communication system comprising: a circuitconfigured to transmit symbols of a digital transmission constellation,the digital transmission constellation belonging to a set of digitaltransmission constellations ordered from a constellation with a smallestnumber of bits per symbol up to a constellation with a greatest numberof bits per symbol, each digital transmission constellation having knownrespective error rate vs. signal-to-noise characteristics, wherein saidcircuit is configured to transmit the symbols of the digitalconstellation by at least identifying a number of bits m of a firstdigital transmission constellation from the set of digital transmissionconstellations that is configured to communicate up to a threshold errorrate β^((T)) and having a greatest signal-to-noise ratio smaller than asignal-to-noise ratio of a received signal γ, identifying a number ofbits {hacek over (m)} of a second digital transmission constellationfrom the set of digital transmission constellations that corresponds toa digital transmission constellation with a number of bits per symbolgreater than that of the first digital transmission constellation,determining a first probability of use 1−P of the first digitaltransmission constellation and a second probability of use P of thesecond digital transmission constellation that would generate anexpected number of received erroneous bits corresponding to thethreshold error rate β^((T)), the second probability of use beingcomplementary to the first probability of use and being determined as afunction of the error rate of the first and second digital transmissionconstellations P_(e) ^((m))(γ) P_(e) ^(({hacek over (m)}))(γ)corresponding to the signal-to-noise ratio of the received signal γ anda number of bits m of the first digital transmission constellation andthe number of bits {hacek over (m)} of the second digital transmissionconstellation, and transmitting a symbol with a digital transmissionconstellation selected randomly between the first and second digitalconstellations according to the first and second probabilities of use1−P, P, respectively.
 14. The communication system of claim 13, whereinthe error rate comprises one of a bit-error-rate and a block-error-rate.15. The communication system of claim 13, wherein said circuit isconfigured to determine the second probability of use P according to thefollowing equation:$P = {\frac{\left( {{P_{e}^{(m)}(\gamma)} - \beta^{(T)}} \right) \cdot m}{{\left( {{P_{e}^{(m)}(\gamma)} - \beta^{(T)}} \right) \cdot m} - {\left( {{P_{e}^{(\overset{\Cup}{m})}(\gamma)} - \beta^{(T)}} \right) \cdot \overset{\Cup}{m}}}\;.}$16. The communication system of claim 13, wherein said circuit isconfigured to determine the second probability of use P by at least:determining a first discrete set of values (Ω) of the signal-to-noiseratio of the received signal; determining a second discrete set ofprobability values ({ P₁ , P₂ , . . . , P_(L) }) of the secondprobability of use; filling in a look-up table of signal-to-noise ratiolimit values for each combination of a value ( P_(i) ) of the seconddiscrete set with a digital transmission constellation of the set ofdigital transmission constellations by at least for each signal-to-noiseratio of the received signal of the first discrete set (Ω) determiningan average number of bits of a symbol to be transmitted as an average ofthe number of bits {hacek over (m)} of a symbol of the second digitaltransmission constellation and the number of bits m of the first digitaltransmission constellation weighted with the second probability of use (P_(i) ) of the second discrete set and the complementary value thereof(1− P_(i) ), respectively, and estimating the error rate correspondingto an average number of bits of a symbol and of a value of the firstdiscrete set, and for the combination of a value ( P_(i) ) of the seconddiscrete set with the digital transmission constellation, storing asignal-to-noise ratio limit value configured to communicate at thethreshold error rate β^((T)); and determining the second probability ofuse P as a function of the signal-to-noise ratio of the received signalγ, by one of reading from the look-up table a probability valuecorresponding to the signal-to-noise ratio of the received signal γ andinterpolating probability values corresponding to the signal-to-noiseratios limit values closest to the signal-to-noise ratio of the receivedsignal γ.
 17. The communication system of claim 13, wherein the set ofdigital transmission constellations comprises at least one of BPSK,QPSK, 8-QAM, 16-QAM, 64-QAM, 256-QAM and 1024-QAM.
 18. The communicationsystem of claim 13, wherein said circuit is configured to transmitsymbols according to a multi-carrier modulation and execute for eachused carrier.
 19. The communication system of claim 13, wherein saidcircuit comprises a powerline transmission circuit.